When each candidate was paired against potential Democratic candidate Hillary Clinton, the poll showed some candidates might be in for a tough race. Cruz would beat Clinton 49 percent to 44 percent, the survey found, and Clinton would beat Perry 48 percent to 44 percent.

The strongest candidate against Clinton in the state was Christie, who would beat the former secretary of state 47 percent to 38 percent.

PPP polled 318 Republican primary voters from June 28 to July 1 for the survey on the GOP primary, which has a margin of error of plus or minus 5.5 percentage points. For the question about the general election, 500 registered voters were surveyed, and the results have an error margin of plus or minus 4.4 percentage points.